The user account I run the computer as is already an administrator account, but if I run photoshopelementseditor.exe as the default administrator account, select the country, Photoshop Elements will open. If I close it and restart it I have to select the country again.

So the registry value is not being written.

This is the only application on my computer where a setting does not save.

I'm not sure what 1 would be, perhaps it's just the first country on the list. All I can say for sure is that US is 244. For most functions, PSE is just looking for whether you are outside the US. If you are, there are different services available, but most of the rest of the world outside the US uses the same stuff. So having 1 probably isn't going to have any effect on your ability to use the application.

Ok I would be curious to see if it is the root cause of your difficulties. Looking at their product page http://www.piriform.com/ccleaner it looks as if does have a registery cleaning function. Perhaps it is identifying this entry incorrectly as not being used.

I have run CCleaner with more cleanup options than I usually do and PSE has not asked for the country on the next startup. I don't regularly run CCleaner, only rarely, so it is not the cause of this problem, which occurs far more frequently than me using CCleaner.

Yea it is difficult to say if it is the cause or not. From the product description it does appear it decides on what should be in the registry and what shouldn't. I would still advise using Regedit to do a backup of your registry before hand. Only takes a moment and can prevent many issues.

Beyond that perhaps just try to run Photoshop Elements regularly and keep an eye out for what was done previously on your system prior to the issue reoccuring. Btw you can also use Regedit to export the modified registry key to make it easier when you do have to put the registry setting back.